Problem: Simplify the following expression: $k = \dfrac{5t^2 - 2t}{2t^2 + 3t} - \dfrac{4rt + 2st}{2t^2 + 3t}$ You can assume $r,s,t \neq 0$.
Answer: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{5t^2 - 2t - (4rt + 2st)}{2t^2 + 3t}$ $k = \dfrac{5t^2 - 2t - 4rt - 2st}{2t^2 + 3t}$ The numerator and denominator have a common factor of $t$, so we can simplify $k = \dfrac{5t - 2 - 4r - 2s}{2t + 3}$